2.306   ODE No. 306

1. Problem in Latex
2. Mathematica input
3. Maple input

$$(y(x{)}^3-x^3)y^{\prime }(x)-x^{2}y(x)=0$$ ✓ Mathematica : cpu = 0.0524991 (sec), leaf count = 201

$$\{\{y(x)\to \sqrt[3]{x^3-\sqrt{x^6-e^{6c_1}}}\},\{y(x)\to -\sqrt[3]{-1}\sqrt[3]{x^3-\sqrt{x^6-e^{6c_1}}}\},\{y(x)\to (-1{)}^{2/3}\sqrt[3]{x^3-\sqrt{x^6-e^{6c_1}}}\},\{y(x)\to \sqrt[3]{\sqrt{x^6-e^{6c_1}}+x^3}\},\{y(x)\to -\sqrt[3]{-1}\sqrt[3]{\sqrt{x^6-e^{6c_1}}+x^3}\},\{y(x)\to (-1{)}^{2/3}\sqrt[3]{\sqrt{x^6-e^{6c_1}}+x^3}\}\}$$

✓ Maple : cpu = 0.353 (sec), leaf count = 381

$$\{y\left(x\right)=x\frac{1}{\sqrt[3]{(-x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=x\frac{1}{\sqrt[3]{-(x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(-\frac{1}{2}-\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{(-x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(-\frac{1}{2}-\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{-(x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(-\frac{1}{2}+\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{(-x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(-\frac{1}{2}+\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{-(x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(\frac{1}{2}-\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{(-x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(\frac{1}{2}-\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{-(x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(\frac{1}{2}+\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{(-x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{x}{{(\frac{1}{2}+\frac{i}{2}\sqrt{3})}^2}\frac{1}{\sqrt[3]{-(x^3\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^6+1})x^3\mathit{\_}\mathit{C}\mathit{1}}}\}$$